In the house north-west of the fountain, you will find this man. Each day he will say that he is feeling the vibes of a certain type. Bring a Pokémon of that type to him and he'll give you a choice of five berries: Cheri, Chesto, Pecha, Rawst, and Aspear.Source

In Pokémon X and Y you can get a Chesto Berry from a man in the North-Western most house in Camphrier Town after you bring him a specific Pokémon that he has asked for. Note the Chesto Berry is the second option that he will offer you. You can do this on a daily basis.

A Chesto Berry may also be randomly obtained from a stall South of the Incense Shop in Coumarine City. Note only one of five berries can be found here daily (Cheri Berry, Chesto Berry, Pecha Berry, Rawst Berry or Aspear Berry) so you will not always get a Chesto Berry every day but it is worth trying your luck.